08 Ultrasound

Axial resolution

Half the spatial pulse length ≈ n λ / 2.

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Simulation

Axial resolution — Change the numbers; the scene follows.

Where it works

Ultrasound

QA phantom

On the tissue-mimicking phantom — axial and lateral resolution are checked here.

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Formula

R_a \approx \frac{n\lambda}{2} = \frac{n c}{2f}

Variables

n · Cycles per pulsef · FrequencyMHzc · Speed of soundm/s

Results

λ
Wavelength
0.308mm
R_a
Axial resolution
0.462mm

Explanation

R_a \approx \frac{n\lambda}{2} = \frac{n c}{2f}

What it means

Axial (depth) resolution is about half the spatial pulse length: n λ / 2. Higher frequency and fewer cycles (more damping, wider bandwidth) improve it. 5 MHz, 3 cycles in tissue → ~0.5 mm. This is a working relation in Ultrasound.

Where it is used

Clinically it sits on the Ultrasound — QA phantom. On the tissue-mimicking phantom — axial and lateral resolution are checked here. Ultrasound equations sit on the probe face and along the beam: impedance, Snell, Doppler, MI and TI. They explain why gel matters, why aliasing appears, and why a mechanical index is on the screen.

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How to use it

Harmonic imaging uses a shorter effective pulse. Axial resolution is usually better than lateral — don’t expect the same number in both directions. Change one input and watch the curve and the simulation follow.

Symbols

nCycles per pulse3
fFrequency5 MHz
cSpeed of sound1,540 m/s

Worked example

A typical case from the default values: n = 3 (Cycles per pulse); f = 5 MHz (Frequency); c = 1,540 m/s (Speed of sound). Substituting into the relation gives λ = 0.308 mm; R_a = 0.462 mm. These are teaching numbers — align them with your machine.

Typical values give

λ = 0.308mm
R_a = 0.462mm

Where it comes from

The displayed formula is the working relation. Half the spatial pulse length ≈ n λ / 2. Usual reference: Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg

Assumptions & limits

Soft-tissue speed 1540 m/s. Damping and the true envelope (not a rectangle of n cycles) set the real SPL. Attenuation may force a lower f at depth.

Pitfalls

Soft-tissue 1540 m/s is an assumption — not a measurement in that patient. Doppler angle 90° gives no shift. MI and TI are on-screen estimates, not absorbed dose. Soft-tissue speed 1540 m/s. Damping and the true envelope (not a rectangle of n cycles) set the real SPL. Attenuation may force a lower f at depth.

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Soft-tissue speed 1540 m/s. Damping and the true envelope (not a rectangle of n cycles) set the real SPL. Attenuation may force a lower f at depth.

In this specialty

Ultrasound